Solution of Plane Hydrofracture Problem by Runge-Kutta Method under Arbitrary Initial Condition
A. M. LINKOV1,2
1Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Bol’shoy Pr. V.O. 61, Saint Petersburg, 199178 Russia
2Saint Petersburg State Politechnic University, ul. Politechnicheskaya 29, 195251, Saint Peterburg, Russia
Keywords: гидравлический разрыв, уравнение скорости, асимптотический зонтик, начальные условия, неньютоновская жидкость, раскрытие, длина трещины, hydraulic fracture, speed equation, asymptotic umbrella, initial conditions, non-Newtonian fluid, opening, fracture length
Abstract
The solution to a hydraulic fracture problem for the model of Khristianovich-Geertsma-de Klerk is obtained on the basis of the modified formulation of the problem, which, in contrast with the conventional approach, employs the particle velocity rather than the flux. This served to complement the system of ordinary differential equations, resulting after spatial discretization, with the speed equation. The complete system is solved by the Runge-Kutta method for arbitrary initial conditions.The decaying influence of the initial conditions on key characteristics of a fracture (opening and length) at the end of a treatment is established and numerically analyzed.
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